Finite Group Databasebeta

← #16786844

Subgroups — #16786844

Order 3328.

314 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131193C212yesmaximal, complemented
2#13129775C212yesmaximal, complemented
3#13129759C212yesmaximal
4#13123481C211yesmaximal, characteristic
5C4×#6127C411yescharacteristic
6C4×C13×M16C411yescharacteristic
7#11718790C411yescharacteristic
8#11718790C2211yescharacteristic
9#11718780C411yescharacteristic
10#11718780C2211yescharacteristic
11C2×C4×#1055C2211yescharacteristic
12#11718370—22no—
13#11718346—22no—
14C22⋊#6092C2214yes—
15C4⋊#6092—22no—
16C4×#6092—22no—
17C2×#6127C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C42×C13C2×C411yescharacteristic
21C4×C22⋊D13—22no—
22#88180C2×C411yescharacteristic
23C22×#1055C2×C411yescharacteristic
24C22×#1055C2311yescharacteristic
25C4×D52C812yes—
26#88126—21no—
27C42×D13—21no—
28C4×Dic26C812yes—
29C2×#6092—24no—
30C13×#97—21no—
31C4×C8×C13—21no—
32#88060—22no—
33#88060—22no—
34#88054—22no—
35#88054—22no—
36C4×#1055D412yes—
37C4×#1055D412yes—
38#11462—131nomaximal, Sylow
39C22×C4×C13M1612yes—
40C22×C4×C13C22×C411yescharacteristic
41C2×C22⋊D13—21no—
42#6127—41no—
43#6127—41no—
44C2×D52C2×C811yescharacteristic
45C2×C4×D13—22no—
46C2×C4×D13—21no—
47C2×Dic26C2×C811yescharacteristic
48C13×M16—41no—
49C13×M16—41no—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C42×C13C22⋊C411yescharacteristic
53C42×C13C22⋊C411yescharacteristic
54C42×C13C2×C812yes—
55C22⋊Dic13—21no—
56#6103—22no—
57C4⋊Dic13C2×C812yes—
58#6101—22no—
59C4×Dic13—22no—
60C4×Dic13—21no—
61C2×#1055—41no—
62C2×#1055—41no—
63C2×#1055C22⋊C412yes—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2922—131no—
67#2162—132no—
68#1323—132no—
69#1315—132no—
70C23×C13C2×M1611yescharacteristic
71C22×D13—21no—
72C2×C4×C13—24no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13C22⋊C812yes—
76C2×C4×C13C22⋊C812yes—
77C2×C4×C13C2×C22⋊C411yescharacteristic
78C2×C4×C13C22×C811yescharacteristic
79C22⋊D13—42no—
80C2×Dic13—21no—
81C2×Dic13—22no—
82D52—41no—
83C4×D13—44no—
84C4×D13—41no—
85C4×D13—41no—
86Dic26—41no—
87C8×C13—41no—
88C8×C13—41no—
89#1055—22no—
90#1055—22no—
91C4×#41—131no—
92#433—262no—
93#431—262no—
94#424—131no—
95#424—131no—
96#408—131no—
97#408—131no—
98C4×M16#26111yescharacteristic
99C2×C4×C8—131no—
100C4⋊C16—262no—
101C22⋊C16—134no—
102C4×C16—262no—
103C22×C13—22no—
104C22×C13—21no—
105C22×C13C2×C22⋊C811yescharacteristic
106C2×D13—42no—
107C2×D13—41no—
108C4×C13—22no—
109C4×C13—21no—
110C4×C13#35014yes—
111C4×C13#41011yescharacteristic
112C4×C13#41311yescharacteristic
113Dic13—42no—
114Dic13—41no—
115C2×#41—131no—
116C2×M16C2×#26111yescharacteristic
117C2×M16C2×#26111yescharacteristic
118C22×C8—131no—
119C22×C8—131no—
120C4×Q8—132no—
121C4×D4—132no—
122C4×D4—262no—
123#117—131no—
124#117—261no—
125C2×C42—261no—
126C2×C42C2×#26111yescharacteristic
127C2×C16—264no—
128C4⋊C8—262no—
129C4⋊C8—262no—
130C22⋊C8—262no—
131C22⋊C8—262no—
132#97—21no—
133C4×C8—21no—
134C4×C8—132no—
135C4×C8—132no—
136C2×C13—41no—
137C2×C13#145811yescharacteristic
138C2×C13C2×#35012yes—
139D13—81no—
140#41—521no—
141#41—521no—
142C2×Q8—131no—
143C2×D4—131no—
144C2×D4—261no—
145C22×C4—262no—
146C22×C4—261no—
147C22×C4#611812yes—
148C22×C4C22×#26111yescharacteristic
149M16—41no—
150M16—41no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—132no—
154C2×C8—132no—
155C2×C8—521no—
156C2×C8—521no—
157C4⋊C4—132no—
158C4⋊C4—262no—
159C22⋊C4—261no—
160C22⋊C4—262no—
161C42—262no—
162C42—261no—
163C42D13⋊C812yes—
164C42C22⋊#26111yescharacteristic
165C42C22⋊#26111yescharacteristic
166C16—524no—
167C13#1146211yescharacteristic, complemented, Sylow
168C23—261no—
169C23C2×#611811yescharacteristic
170Q8—521no—
171D4—521no—
172D4—522no—
173C2×C4—24no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—262no—
177C2×C4—261no—
178C2×C4—524no—
179C2×C4—521no—
180C2×C4—521no—
181C2×C4#8811112yes—
182C2×C4#8811112yes—
183C2×C4C2×D13⋊C811yescharacteristic
184C2×C4C2×C22⋊#26111yescharacteristic
185C8—41no—
186C8—41no—
187C8—262no—
188C8—262no—
189C22—22no—
190C22—21no—
191C22—522no—
192C22—521no—
193C22C2×#8811111yescharacteristic
194C4—22no—
195C4—21no—
196C4—522no—
197C4—521no—
198C4#1171827014yes—
199C4#1171911611yescharacteristic
200C4#1171913211yescharacteristic
201C2—41no—
202C2—1041no—
203C2#1313006911yescharacteristic
204C2C2×#1171827012yes—
subgroupG/H
centerC42C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC4×C13×M16C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#6127C2×C4
cosocleC22×#1055C23
hypercenterC4×M16#261
hypocenterC13#11462
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13131193C2semidirect
2. #13129775C2semidirect
167. C13#11462semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131311932
#131297752
#131297592
#131234812
#1146213